Using zeros to graph polynomials

Using zeros to graph polynomials
Description
Exercise Name:	Using zeros to graph polynomials
Math Missions:	Algebra II Math Mission, Mathematics III Math Mission
Types of Problems:	3

The Using zeros to graph polynomials exercise appears under the Algebra II Math Mission and Mathematics III Math Mission. This exercise emphasizes the connection between the algebraic "zero" of a function and the geometric "x-intercept."

Types of Problems

There are three types of problems in this exercise:

1. Determine the graph of the given function: This problem provides a function and several graphs. The user is asked to determine which graph displays the function.

   

   Determine the graph of the given function

2. Determine all functions that could be the graph: This problem provides a graph and several possible functions. The user is asked to determine all of the functions that could possibly represent the graph.

   

   Determine all functions that could be the graph

3. Plot the x-intercepts: This problem provides a function and a coordinate plane. Users are expected to find the zeroes of the function and plot only these, as x-intercepts, on the plane.

   

   Plot the x-intercepts

Strategies

Knowledge of graphing and some of the polynomial theorems are encouraged to ensure success on this exercise.

1. A zero of an equation is an x-intercept of it's graph.
2. A polynomial with an x-intercept of ${(r,0)}$ will have a factor of ${(x-r)}$ and the remainder when divided by ${(x-r)}$ will be zero.

Real-life Applications

1. Graphing is an important concept in calculus and beyond that can be made easier with advanced techniques for graphing. Recognizing the connection between a factored polynomials and it's zeroes helps this application.